Consider historical data showing that the average annual rate of return on the S

Question

Consider historical data showing that the average annual rate of return on the S&P; 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P; 500 standard deviation has been about 29% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P; 500 index with weights as follows: (Leave no cells blank - be certain to enter "0" wherever required. Round "Expected Return" to 1 decimal place and the "Variance" to 4 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

Rate of Return on T-Bill, rbills = 4%

Expected Rate of Return on Index, rindex = 8% + 4% = 12%

Standard Deviation of the Index, SDindex = 29%

Standard Deviation of the T-Bill, SDbills = 0% ,since it is risk free.

Expected rate of return on potfolio =Windex * rindex + Wbills * rbills

Vairance of the Portfolio = Windex2* SDindex2 + Wbills2* SDbills2 + 2 * Windex* Wbills * COVindex,bills

                                       = windex2* SDindex2 (since Standard Deviation of T-Bills is 0)

Using the above formulas, the expected returns and variances are calculated as

W bills W index Expected Return Formula Expected Return Variance Formula Variance 0.2 0.8 0.2 * 4% + 0.8 * 12% 10.4 0.8^2 * 0.29^2 0.0538 0 1 0.0 * 4% + 1 * 12% 12.0 1^2 * 0.29^2 0.0841 0.6 0.4 0.6 * 4% + 0.4 * 12% 7.2 0.4^2 * 0.29^2 0.0135 0.8 0.2 0.8 * 4% + 0.2 * 12% 5.6 0.2^2 * 0.29^2 0.0034 0.4 0.6 0.4 * 4% + 0.6 * 12% 8.8 0.6^2 * 0.29^2 0.0303 1 0 1 * 4% + 0.0 * 12% 4.0 0.0^2 * 0.29^2 0.0000

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